Last visit was: 19 Nov 2025, 06:40 It is currently 19 Nov 2025, 06:40
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,388
Own Kudos:
778,227
 [41]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,388
Kudos: 778,227
 [41]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 04:11
2
Kudos
Add Kudos
37
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

76% (02:04) correct 24% (02:13) wrong based on 1440 sessions

History

Date
Time
Result
Not Attempted Yet

Competition Mode Question



If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
ShowHide Answer
Official Answer
C
Most Helpful Reply
avatar
phucduy284
avatar
Joined: 25 Jul 2019
Last visit: 05 Aug 2020
Posts: 2
Own Kudos:
8
 [8]
Given Kudos: 2
Posts: 2
Kudos: 8
 [8]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 10:22
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

5(A-B) = 23+2B
Least possible value of B is 1 => Least possible value of 5(A-B) is 23+2=25
IMO C
avatar
vg18
avatar
Joined: 30 Nov 2017
Last visit: 17 Mar 2021
Posts: 60
Own Kudos:
83
 [8]
Given Kudos: 95
GMAT 1: 690 Q49 V35
GMAT 1: 690 Q49 V35
Posts: 60
Kudos: 83
 [8]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 05:07
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
5A -7(B + 3) = 2
5A-7B-21=2
5A-7B=23

As A and B are positive intergers and from answer choices we know that A>B. lets do trial and error:
Lets say A=5, then B=-ve. not possible
Say A=6, then B=1
Therefore, A-B=5
Ans: C
General Discussion
User avatar
sampriya
User avatar
ISB School Moderator
Joined: 23 Nov 2018
Last visit: 25 Nov 2022
Posts: 301
Own Kudos:
264
 [2]
Given Kudos: 358
Location: India
Schools: Schulich Sept '23 HEC Jan'22 Intake (D) INSEAD Jan 22 intake Erasmus RSM "22 (D) Ivey '22 (D) ISB '23 (I) NUS '23 (D)
GMAT 1: 710 Q48 V39
GPA: 2.88
Products:
My Reviews
Schools: Schulich Sept '23 HEC Jan'22 Intake (D) INSEAD Jan 22 intake Erasmus RSM "22 (D) Ivey '22 (D) ISB '23 (I) NUS '23 (D)
GMAT 1: 710 Q48 V39
Posts: 301
Kudos: 264
 [2]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 06:00
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
5A-7B=23

A and B are positive integers

5(6)-7(1)=23 (A=6, B=1)

A-B= 5

option C is the correct option
User avatar
madgmat2019
User avatar
Joined: 01 Mar 2019
Last visit: 17 Sep 2021
Posts: 584
Own Kudos:
616
 [1]
Given Kudos: 207
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Products:
My Reviews
GMAT 1: 580 Q48 V21
Posts: 584
Kudos: 616
 [1]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 08:24
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
5A -7(B + 3) = 2,

Least value of B=1....then A=6

The least possible value of A-B=5


OA:B

Posted from my mobile device
User avatar
ShankSouljaBoi
User avatar
Joined: 21 Jun 2017
Last visit: 17 Apr 2024
Posts: 622
Own Kudos:
603
 [3]
Given Kudos: 4,090
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Products:
My Reviews
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 3: 650 Q48 V31
Posts: 622
Kudos: 603
 [3]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea Updated on: 26 Dec 2019, 05:05
Originally posted by ShankSouljaBoi on 01 Nov 2019, 13:30.
Last edited by ShankSouljaBoi on 26 Dec 2019, 05:05, edited 1 time in total.
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Substitutefrom given eauation, the value of A into A-B
We get A-B = (23+2B)/5 . For this expression to be minimum B must be minimum which is 1.
Hence expression = [23 + 2(1) ]/5 = 5 = C

Posted from my mobile device
User avatar
kk47
User avatar
Joined: 21 Sep 2016
Last visit: 25 Aug 2025
Posts: 26
Own Kudos:
24
 [2]
Given Kudos: 192
GMAT 1: 610 Q47 V27
GMAT 1: 610 Q47 V27
Posts: 26
Kudos: 24
 [2]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 13:47
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
As per the question,

5A - 7B -21 = 2
=> 5A - 7B = 23
=> 5(A-B) = 23 + 2B
=> A-B = (23+2B)/5
Since A and B are positive integers and we have to find the minimum value of A-B, we have to consider the minimum possible value of B as per the previous expression.

Min. B = 1
Therefore, min. (A-B) = 5
Answer is (C)

Posted from my mobile device
User avatar
lacktutor
User avatar
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 659
Own Kudos:
1,395
 [3]
Given Kudos: 69
Posts: 659
Kudos: 1,395
 [3]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 14:46
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
A, B — positive integer
5A —7(B+3)= 2
—> what is the least possible value of A —B =???

5A —7B —21=2

5A —5B —2B =23

5*( A—B)= 23+ 2B

A —B= (23+ 2B)/5
—> in order A—B to be the least value, B should be equal to 1.

B=1 —> A —B = (23+2)/5= 5

The answer is C

Posted from my mobile device
User avatar
BelalHossain046
User avatar
Joined: 11 Feb 2013
Last visit: 05 Apr 2023
Posts: 198
Own Kudos:
314
 [1]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
Posts: 198
Kudos: 314
 [1]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 01 Nov 2019, 15:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
C is my answer.

5A -7(B + 3) = 2
or, 5A=23+7B.
Min value of B=1, So min value A=6
So min value (A-B)=5
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 19 Nov 2025
Posts: 1,292
Own Kudos:
4,268
 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,292
Kudos: 4,268
 [1]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 02 Nov 2019, 01:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
5A -7(B + 3) = 2
--> 5A - 7B = 23
--> 5A - 5B = 2B + 23
--> A - B = (2B + 23)/5

Least possible value of A - B is when B = 1
--> A - B = (2*1 + 23)/5 = 25/5 = 5

IMO Option C
avatar
suchithra
avatar
Joined: 31 Oct 2015
Last visit: 14 Oct 2022
Posts: 89
Own Kudos:
118
 [1]
Given Kudos: 179
Posts: 89
Kudos: 118
 [1]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 02 Nov 2019, 13:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given : 5A -7(B + 3) = 2 and A,B are positive integers

5A - 7B - 21 = 2
5A - 7B = 23
5A - 5B -2B = 23
5(A-B) = 23 + 2 since the least positive value of B is 1
5(A-B) = 25
A-B = 5

Answer is C
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,684
Own Kudos:
1,447
 [1]
Given Kudos: 607
Location: United States
Posts: 1,684
Kudos: 1,447
 [1]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 03 Nov 2019, 15:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Show more

5A -7(B + 3) = 2
5A -7B = 2 + 21
5A = 23 + 7B
A = (23 + 7B) / 5

(A,B) = positive integers
A = (23 + 7B) / 5 = positive integer
B = 1; A = 23+7/5 = 30/5 = 6
B = 2; A ≠ integer
B = 6; A = 23+7(6)/5 = 65/3 = 13…

min. A-B = 6-1 = 5

Answer (C)
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 Nov 2025
Posts: 5,794
Own Kudos:
5,509
 [2]
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,794
Kudos: 5,509
 [2]
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 13 Dec 2019, 07:36
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Competition Mode Question



If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Show more

5A -7(B + 3) = 2
5A-7B = 23
B = (5A-23)/7
When A=6; B=1; A-B = 5
When A=13;B=6; A-B =7
A-B increases further e.g. A=20;B=11; A-B = 9

IMO C
avatar
Avysar
avatar
Joined: 25 Apr 2020
Last visit: 29 Aug 2020
Posts: 42
Own Kudos:
80
Given Kudos: 1
Posts: 42
Kudos: 80
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 04 May 2020, 09:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A and B are positive integers
5A-7(B+3)=2
So 5A-7B=2+21=23
Rewriting, 5(A-B)-2B=23
5(A-B)= 23+2B
Since we want the least answer, let us start with the least value for B say 1
5(A-B)= 23+2=25
so A-B=5
Hence C

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea 23 Aug 2025, 10:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105388 posts
Krunaal
Tuck School Moderator
805 posts